Question

Suppose the parallelogram on the coordinate plane is dilated in reference to the origin using a scale factor of 3. What would be the coordinates of the new vertices of E′F′G′H′
?(7 points)
Responses

E′(−13,53), F′(23,83), G′(43,43),
and H′(13,13)
E′(−13,53), F′(23,83), G′(43,43),
and cap h prime times open paren 1 third comma 1 third close paren

E′(−4,2), F′(−1,5), G′(1,1),
and H′(−2,−2)
E′(−4,2), F′(−1,5), G′(1,1),
and cap h prime times open paren negative 2 comma negative 2 close paren

E′(2,8), F′(5,11), G′(7,7),
and H′(4,4)
E′(2,8), F′(5,11), G′(7,7),
and cap h prime times open paren 4 comma 4 close paren

E′(−3,15), F′(6,24), G′(12,12),
and H′(3,3)

Answer 1

ok e -1,5 f2,8 g4,4 h 1,1

Answer 2

To dilate a figure in the coordinate plane from the origin using a scale factor of \( k \), you multiply each of the original vertices by \( k \). In this case, the scale factor is 3.

Let's denote the original vertices of the parallelogram as follows:
- \( E(x_1, y_1) \)
- \( F(x_2, y_2) \)
- \( G(x_3, y_3) \)
- \( H(x_4, y_4) \)

After being dilated by a scale factor of 3, the coordinates of the new vertices will be:
- \( E'(3x_1, 3y_1) \)
- \( F'(3x_2, 3y_2) \)
- \( G'(3x_3, 3y_3) \)
- \( H'(3x_4, 3y_4) \)

Since you didn't provide the original coordinates of the vertices E, F, G, and H, I can't calculate the new coordinates for E', F', G', and H' directly from the information provided. However, I can analyze the multiple-choice options you gave based on the concept of dilation.

1. **Option Analysis**:
- E′(−13, 53), F′(23, 83), G′(43, 43), and H′(13, 13)
- E′(−13, 53), F′(23, 83), G′(43, 43), and H′(1/3, 1/3)
- E′(−4, 2), F′(−1, 5), G′(1, 1), and H′(−2,−2)
- E′(−4, 2), F′(−1, 5), G′(1, 1), and H′(−2,−2)
- E′(2, 8), F′(5, 11), G′(7, 7), and H′(4, 4)
- E′(2, 8), F′(5, 11), G′(7, 7), and H′(4, 4)
- E′(−3, 15), F′(6, 24), G′(12, 12), and H′(3, 3)

To determine the new coordinates, you must check which set of coordinates corresponds to the transformation of the original vertices by multiplying by 3.

2. If you have the original coordinates of the vertices or if there’s additional information about the original shape, I can help you confirm the final set of transformed coordinates. Without the original coordinates, however, we can't identify the exact new vertices based merely on the given response options.

If you can provide the original vertices E, F, G, and H, I would be able to perform the dilation and identify the correct response from your options.

Answer 3

Thank you for providing the original coordinates of the vertices. The original vertices of the parallelogram are:

- \( E(-1, 5) \)
- \( F(2, 8) \)
- \( G(4, 4) \)
- \( H(1, 1) \)

To dilate these vertices from the origin using a scale factor of \( k = 3 \), we multiply each coordinate by 3.

### Dilation Calculations:
- **For \( E \):**
\[
E' = (3 \cdot -1, 3 \cdot 5) = (-3, 15)
\]

- **For \( F \):**
\[
F' = (3 \cdot 2, 3 \cdot 8) = (6, 24)
\]

- **For \( G \):**
\[
G' = (3 \cdot 4, 3 \cdot 4) = (12, 12)
\]

- **For \( H \):**
\[
H' = (3 \cdot 1, 3 \cdot 1) = (3, 3)
\]

### New Coordinates:
The new vertices after dilation will be:
- \( E'(-3, 15) \)
- \( F'(6, 24) \)
- \( G'(12, 12) \)
- \( H'(3, 3) \)

### Matching with Options:
Now we can look at the provided options to see which one matches the new vertices \( E', F', G', H' \):
- **Option: E′(−3, 15), F′(6, 24), G′(12, 12), and H′(3, 3)**

This matches perfectly with our calculated new coordinates.

**So the correct response is:**
**E′(−3, 15), F′(6, 24), G′(12, 12), and H′(3, 3)**.